A multi-thermogram-based Bayesian model for the determination of the thermal diffusivity of a material
| Autor: | Peter M. Harris, Jérémie Mattout, D. Rochais, Louise Wright, Bruno Hay, Nicolas Fischer, Géraldine Ebrard, Alexandre Allard |
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| Rok vydání: | 2015 |
| Předmět: |
Markov chain
Bayesian probability General Engineering 02 engineering and technology Inverse problem 021001 nanoscience & nanotechnology Bayesian inference Thermal diffusivity 01 natural sciences 010309 optics 0103 physical sciences Prior probability Statistics Measurement uncertainty Sensitivity (control systems) Statistical physics 0210 nano-technology Mathematics |
| Zdroj: | Metrologia. 53:S1-S9 |
| ISSN: | 1681-7575 0026-1394 |
| DOI: | 10.1088/0026-1394/53/1/s1 |
| Popis: | The evaluation of the thermal diffusivity is at the heart of modern materials characterisation. The determination of the associated uncertainty is difficult because such an evaluation is performed in an indirect way, in the sense that the thermal diffusivity can not be measured directly. Indeed, the well known GUM uncertainty framework does not provide a reliable evaluation of measurement uncertainty for such inverse problems, because the underlying measurement model is supposed to be a direct relationship between the measurand (the quantity to be measured) and the input quantities. This paper is concerned with the development of a Bayesian approach to evaluate the measurement uncertainty associated with the thermal diffusivity. The Bayesian model is first developed for a single thermogram and is extended to the case of several thermograms organized as a repeatability/reproducibility structure. This multi-thermograms based model is able to take into consideration a larger set of influent quantities that occur during the measurements and yields a more reliable uncertainty evaluation than that obtained for a single thermogram. Different aspects of the Bayesian model are discussed (sensitivity to the choice of the prior distribution, the Metropolis-Hastings algorithm used for the inference, the convergence of the Markov chains). |
| Databáze: | OpenAIRE |
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